With regards to second order phase transitions, Landau put forward a phenomenological Hamiltonian which captures essential aspects of the transition in the infrared limit of the system [1]}. His formalism suggests that near the critical temperature \(T_C\)  (the temperature at which phase transition takes place), the Hamiltonian can be expanded in terms of a local order parameter \(\phi (x)\)  on the basis of appropriate symmetries. For example, if a system has a \(Z_2\)  symmetry i.e. it is symmetric under \(\phi (x) \rightarrow -\phi (x)\) ; then for \(T \approx T_C\)  and a small external coupling field \(h\) , the Hamiltonian \(H(\phi )\)  can be expressed as follows:
\(\beta H =\int d^dx\left(\frac{K}{2}(\phi )^2 + t \phi ^2(x) + u \phi ^4(x) + \dots - h.\phi (x) \right)\) 
